I've had a look into it, and it doesn't work if you try to do it mathmatically. You always need more than 3 gos on the seesaw.

There is a solution in the replies to my original comment that is the actual solution, and it works every time and is much simpler than any grouping method.

It involves assigning a letter to each person and then aligning that with a grid of positions "left" or "right" or "none" on the seesaw. Over the three rounds. So, person A is on the right all three rounds person b is on the right for 2 rounds then on the left for the 3rd round.

You end up with a list of 12 patterns that do not repeat or mirror any other pattern like "LLL" "LLR" "LRR" "LR-" etc. Then you do all three rounds and compare the position the seesaw was in with those patterns.

If the seesaw was down on the left 2 times the down on the right the third time then you look for which person had that pattern in this case it was person B. So they are the one with a different weight and they were heavier.

Equally, if the opposite pattern occurred. It was down on the right 2 times, then down on the left for round, then that is the opposite pattern of person B and does not occur anywhere else, so it was person B, and they were lighter.

person:  A B C D E F G H I J K L

round 1: L L L L R R R R — — — -

round 2: L L R R R — — — L R L -

round 3: L R R — — L R — L L — R